Development of a Gauss-Chandrasekhar Quadrature for the Boundary Sources Method with Anisotropic Scattering

Abstract

It was recently shown that solving neutron transport multislab problems by the boundary source (BS) method leads to spectral accuracy. The BS method is, however, computationally expensive because it needs the numerical evaluation of a large number of double angular moments, which are double integrals of a product of Chandrasekhar polynomials with a complicated weight function presenting a variety of singularities. We develop a Gauss-Chandrasekhar quadrature method that leads to substantial reduction of the Central Processing Unit (CPU) time spent in the evaluation of these integrals, thus greatly reducing the cost of the BS method.

Keywords:

• Neutron transport operator
• Discrete spectrum
• Quadrature